CN103973439B - A kind of multi-variable public key ciphering method - Google Patents

Abstract

The invention discloses a kind of multi-variable public key ciphering method.In key generation process, using alternative manner structural matrix, substantially reduce the length of key, be easy to key management；Using probability encryption, random parameter is introduced in encryption, decryption side must solve this random parameter by decrypting process, and participate in the deciphering of plaintext, only know the correct decrypted plaintext of size ability of random parameter, increased the difficulty that attacker cracks ciphertext, even if ciphertext is also different in the case of public key identical, public key can be announced in the form of similar telephone number, improves cryptographic security；Based on Combinatorial Optimization difficult problem and multivariate quadratic polynomial problem, the attack of quantum computer can be resisted, encryption/decryption speed is fast, can apply to mobile terminal, such as mobile phone etc.；Based on the computing on finite field, simplify calculating process；There is additive homomorphism and subtraction homomorphism, under specific condition, there is multiplicative homomorphic, can apply to the emerging fields such as cloud computing.

Description

A kind of multi-variable public key ciphering method

Technical field

The invention belongs to field of information security technology, more particularly, to a kind of multi-variable public key ciphering method.

Background technology

With the continuous development of cyber-net, people to the integrity of information, security requirement more and more higher, because This, cryptography is arisen at the historic moment.Public key cryptography is different due to its encryption key and decruption key, becomes solution network security Key means with some safety problems of information security.But it is as the continuous development of information technology, the property to system for the people More and more higher can be required, not only the integrity of require information, safety, also require the simplicity of transmission information process and quick Property.

At present, the key management of main flow symmetric cryptography and transmittance process are more complicated, and the operation efficiency of public key cryptography is low, The growing material and cultural needs of people increasingly can not be met.Secondly, apply with mobile phone or mobile radio terminal Popularization, the proposition of non-support cable concept, and the development of Internet of Things, mobile phone or mobile radio terminal are played the part of in our lives Role more and more important, but the speed of service of mobile phone or mobile radio terminal all also cannot be compared with computer with resource, Therefore, under the applicable cases limited by this resource environment such as mobile phone or mobile radio terminal, traditional encipherment scheme is no longer suitable With.Additionally, with the proposition of quantum calculation, traditional encipherment scheme is greatly threatened, once the success of quantum computer Research and development, public key cryptography RSA, ECC that people commonly use will be no longer safe.

The public key encryption method that anti-quantum computer is attacked mainly has NTRU algorithm based on lattice problem, is based on Hash function Signature algorithm, the public-key cryptosystem based on error correcting code and multivariate quadratic polynomial (abbreviation MQ) public-key cryptosystem and OUT2000 public-key cryptosystem etc., the convenience of these algorithms and safety, are highly suitable for the mobile terminals such as smart card.Public The number of opening is that the Chinese patent application of CN103200001A discloses a kind of multi-variable public key ciphering method, has and realizes efficiency high, The feature that anti-quantum computer is attacked.Even so, the key that said method all has storage is longer, it is not easy to key management Problem.Therefore, in order to public key cryptography can preferably be developed, preferably apply in life, be badly in need of research safety quick Public key algorithm.

Content of the invention

Disadvantages described above for prior art or Improvement requirement, the invention provides a kind of multi-variable public key ciphering method, Substantially reduce the length of key, be easy to key management, introduce random parameter in encryption, be a kind of method of probability encryption, Only know the correct decrypted plaintext of size ability of random parameter, increased the difficulty that attacker cracks ciphertext, quantum can be resisted The attack of computer, encryption/decryption speed is fast, can apply to mobile terminal, such as mobile phone etc..

For achieving the above object, the invention provides a kind of multi-variable public key ciphering method is it is characterised in that include as follows Step：

(1) generate key, further include following steps：

Choose k integer p in finite field Z and finite field Z₁,p₂,…,p_i,…,p_k, wherein, i is the just whole of no more than k Number；Following integer is chosen on finite field Z：(β₁₁,β₁₂),(β₂₁,β₂₂),…,(β_i1,β_i2),…,(β_k1,β_k2) and (x₁, x₂,…,x_i,…,x_k)；Construction and (β₁₁,β₁₂),(β₂₁,β₂₂),…,(β_i1,β_i2),…,(β_k1,β_k2) and p₁,p₂,…,p_i,…, p_kTwo groups of related parameters a₁₁,a₂₁,…,a_i1,…,a_k1And a₁₂,a₂₂,…,a_i2,…,a_k2, make a_i1And a_i2Binary length Identical；

Construction k × n dimension non-singular matrix A=(a_ij), j=1 ..., n, wherein, j>When 2,

Structural matrix K_l×kAnd matrix D_k×lSo as to meet D K=λ E_k×k, and l >=k, wherein, E_k×kIt is unit matrix, λ is arbitrary integer；

Calculating matrix C=K A=(c_yj), y=1 ..., l, chooses positive integer h, 0 ＜ h ＜ n, determines random parameter ε's Span [1, e], wherein,T is any positive integer；

Choose l integer P 1 ..., Pl, meet inequalityObtain P₁,...,P_lLeast common multiple N；

Solve congruence equationsObtain vectorial d=(d₁,d₂..., d_j,…,d_n)；

By d and h together as public key, or by d, h and N together as public key, corresponding private key at least includes (x₁, x₂,…,x_i,…,x_k)、p₁,p₂,…,p_i,…,p_k、P₁,...,P_l、(β₁₁,β₁₂),(β₂₁,β₂₂),…,(β_i1,β_i2),…,(β_k1, β_k2) and D；

(2) use public key encryption, further include following steps：

Obtain plaintext M=(m₁,…,m_n), selected random parameter ε；

The public key being obtained with step (1) is encrypted to plaintext in the way of probability encryption, obtains ciphertext C；

(3) deciphered with private key, further include following steps：

Solve congruence equations

Calculate [S_A1…S_Ak]^T=D [C_P1…C_Pl]^T；

Random parameter ε is obtained by decryption method or synchronous method；

By (S_A1,…,S_Ak) and random parameter ε solve obtain plaintext M=(m₁,…,m_n).

Preferably, in described step (1), a_i1=β_i1p_i,

Preferably, in described step (1), a_i1=β_i1, a_i2=β_i2p_i.

Preferably, described ciphertext C is obtained by any one in following expression：

With

Preferably, obtain random parameter ε by decryption method to be specially：

Calculate congruence equationsObtain random parameter ε, wherein, | λ | represents integer λ Absolute value,The i-th row all elements sum for matrix D.

In general, by the contemplated above technical scheme of the present invention compared with prior art, there is following beneficial effect Really：

(1) in key generation process, using alternative manner structural matrix, substantially reduce the length of key, be easy to close Key manages.

(2) adopt probability encryption, in encryption introduce random parameter, decryption side must by decrypting process solve this with Machine parameter, and participate in the deciphering of plaintext, only know the correct decrypted plaintext of size ability of random parameter, increased deciphering or attack The person of hitting cracks the difficulty of ciphertext, even if ciphertext is also different in the case of public key identical, public key can be to be similar to telephone number Form announce, improve cryptographic security.And the random parameter in common probability public key is directly to be filtered by certain means Remove, decrypting ciphertext is unrelated with this random parameter, so that the difficulty cracking ciphertext is reduced.

(3) it is based on Combinatorial Optimization difficult problem and multivariate quadratic polynomial (MQ) problem, quantum computer can be resisted Attack, encryption/decryption speed is fast, can apply to mobile terminal, such as mobile phone etc..

(4) based on the computing on finite field, rather than based on the computing on multinomial, simplify calculating process.

(5) there is additive homomorphism and subtraction homomorphism, under specific condition, there is multiplicative homomorphic, can apply to cloud computing etc. new Emerging field.

Brief description

Fig. 1 is public key encryption method application principle schematic diagram in the communications；

Fig. 2 is the multi-variable public key ciphering method flow chart of the embodiment of the present invention.

Specific embodiment

In order that the objects, technical solutions and advantages of the present invention become more apparent, below in conjunction with drawings and Examples, right The present invention is further elaborated.It should be appreciated that specific embodiment described herein is only in order to explain the present invention, and It is not used in the restriction present invention.As long as additionally, involved technical characteristic in each embodiment of invention described below The conflict of not constituting each other just can be mutually combined.

Fig. 1 is public key encryption method application principle schematic diagram in the communications, as shown in figure 1, user passes through key opposite Grow up to be a useful person generation public private key pair, public key be sent to trusted third party, by trusted third party be fabricated to public key cryptography this, and be sent to Each user.Here trusted third party can be analogous to mobile, this trusted third party of UNICOM.The processor of user was both Can be encryption equipment can also be decipher, when user as encryption side, communication initiator when, its corresponding processor is used as Encryption equipment, when user is as decryption side, the recipient of communication, its corresponding processor is used as decipher.Differentiate that processor is used Making encryption or the method for decryption processing is to see the input mode of its information, if information is to input from transmission/receptor, Then processor is used as decipher, if information is from other channels (as keyboard etc.) input, processor is used as encryption equipment.

When user A will be communicated with user B, user A passes through to inquire about public key cryptography originally, and the public key obtaining targeted customer B is close Code public key B8；The random number of public key B8, plaintext A6 and randomizer A2 generation, as input, is input to as encryption In the processor A1 of device.Processor A1 obtains ciphertext C by encryption, and ciphertext C of output is sent out by transmission/receptor A7 and channel Give user B.User B by transmission/receptor B7, ciphertext C is input in processor B1, and processor B1 is used as decipher.Place Reason device B1 is decrypted by calling the private key private key B4 of user B, obtains plaintext B6.When user B will be communicated with user A When, principle is identical, does not just repeat herein.

As shown in Fig. 2 the multi-variable public key ciphering method of the embodiment of the present invention comprises the steps：

(1) generate key, further include following steps：

Choose k integer p in finite field Z and finite field Z₁,p₂,…,p_i,…,p_k, wherein, i is the just whole of no more than k Number；Following integer is chosen on finite field Z：(β₁₁,β₁₂),(β₂₁,β₂₂),…,(β_i1,β_i2),…,(β_k1,β_k2) and (x₁, x₂,…,x_i,…,x_k)；Construction and (β₁₁,β₁₂),(β₂₁,β₂₂),…,(β_i1,β_i2),…,(β_k1,β_k2) and p₁,p₂,…,p_i,…, p_kTwo groups of related parameters a₁₁,a₂₁,…,a_i1,…,a_k1And a₁₂,a₂₂,…,a_i2,…,a_k2So that a_i1And a_i2Binary system long Degree is identical, specifically, a_i1=β_i1p_i,Or a_i1=β_i1, a_i2=β_i2p_i；

Construction k × n dimension non-singular matrix A=(a_ij), j=1 ..., n, wherein, j>When 2,

Structural matrix K_l×kAnd matrix D_k×lSo as to meet D K=λ E_k×k, and l >=k, wherein, E_k×kIt is unit matrix, λ is arbitrary integer；

Calculating matrix C=K A=(c_yj), wherein, y=1 ..., l, choose positive integer h, wherein, 0 ＜ h ＜ n, determine with The span [1, e] of machine parameter ε, wherein,T is any positive integer；

Choose l integer P 1 ..., Pl, meet inequalityObtain P₁,...,P_lLeast common multiple N；

Solve congruence equationsObtain vectorial d=(d₁,d₂,…,d_j,…,d_n)；Specifically, such as Fruit P₁,...,P_lCoprime two-by-two, then d can be solved by Chinese remainder theorem_j；If P₁,...,P_lIt is not coprime two-by-two, then may be used To calculate d by other methods_j；

By d and h together as public key k_p, or by d, h and N together as public key k_p, corresponding private key k_sAt least include (x₁,x₂,…,x_i,…,x_k)、p₁,p₂,…,p_i,…,p_k、P₁,...,P_l、(β₁₁,β₁₂),(β₂₁,β₂₂),…,(β_i1,β_i2),…, (β_k1,β_k2) and D；

(2) use public key encryption, further include following steps：

Obtain plaintext M=(m₁,…,m_n), selected random parameter ε；

The public key being obtained with step (1) is encrypted to plaintext in the way of probability encryption, obtains ciphertext C；Specifically, C Can be obtained by any one in following expression：

(3) deciphered with private key, further include following steps：

Solve congruence equations

Calculate [S_A1…S_Ak]^T=D [C_P1…C_Pl]^T；

Random parameter ε is obtained by decryption method or synchronous method；Specifically, if using formula (1) or formula (2) plus Close mode, typically obtains random parameter ε by synchronous method, if using the cipher mode of formula (3) or formula (4), typically passed through Decryption method obtains random parameter ε；Obtain random parameter ε by decryption method to be specially：

Calculate congruence equationsObtain random parameter ε, wherein, | λ | represents integer λ Absolute value,The i-th row all elements sum for matrix D；

By (S_A1,…,S_Ak) and random parameter ε solve obtain plaintext M=(m₁,…,m_n).

For making those skilled in the art more fully understand the present invention, with reference to specific embodiment, changeable to the present invention Amount public key encryption method is described in detail.It should be noted that following embodiments are only the preferred embodiment of the inventive method, In embodiment, the realization order of each step should not be construed as limitation of the present invention.

Embodiment 1

Random parameter ε is obtained by decryption method, this method comprises the steps：

(1) generate key.Further include following steps：

(1-1) adopt iterative manner construction k × n dimension non-singular matrix A.Further include following steps：

(1-1-1) determine k=2.

(1-1-2) 2 integer p in finite field Z, and finite field Z are chosen₁, p₂.

(1-1-3) choose the following integer on finite field Z：(β₁₁,β₁₂)、(β₂₁,β₂₂) and (x₁,x₂).Make a₁₁=β₁₁p₁,a₂₁=β₂₁p₂,

(1-1-4) structural matrix A=(a_ij), wherein, i=1,2, j=1 ..., n, j>When 2,

(1-2) pass through to obscure or diffusion way F obtains vectorial d=(d₁,d₂,…,d_j,…,d_n), wherein, d_jBy as follows Mode solves：

(A1) choose integer t, s, γ, c, δ, h are so as to meet following 3 conditions simultaneously：(a)γc-δ<max(s,t)<δ； (b)2.2<h<n-2；(c)gcd(R₁,R₃)=1.Wherein, R₁=δ (X+Y) m+c, R₃=1+ γ (X+Y) m, m=p₁p₂- 1, e= tp₁p₂-1.

Wherein,

Choose positive integer R₂, make R₂|(R₁- 1), gcd (R₂,R₃)=1, and R₂>C, structural matrix K_3×2And matrix D_2×3, choosing Select any positive integer z₁, z₂.

(A2) calculating matrix C=K A=(c_yj), y=1,2,3.

(A3) 3 integer P are chosen₁=R₁, P₂=R₂R₃, P₃=R₁R₃.

(A4) congruence equations are solvedIf P₁、P₂And P₃It is not mutual two-by-two

Element, specific formula for calculation is：

d_j=(s+ γ R₁-R₁R₃δ)a_1j+(s+t+γR₁-R₁R₃δ)a_2jmodN

(1-3) by d=(d₁,...,d_n), N=R₁R₂R₃With h together as public key, by β₁₁,β₁₂,β₂₁,β₂₂,D,P₁,P₂, P₃,p₁,p₂,x₁,x₂Together as corresponding private key.

(2) use public key encryption.Further include following steps：

(2-1) obtain plaintext M=(m₁,m₂,…,m_j,…,m_n), selected random parameter ε；

(2-2) public key being obtained with step (1) is encrypted to plaintext, and obtaining ciphertext C is：

(3) deciphered with private key.Further include following steps：

(3-1) congruence equations are solved

(3-2) calculate

(3-3) ε is obtained by decryption method.

Specifically, calculate?Obtaining ε is Mould tp₁p₂Under unique solution.

(3-4) pass through S_A1,S_A2Solve with ε and obtain plaintext M=(m₁,m₂,…,m_j,…,m_n).Further include to walk as follows Suddenly：

(3-4-1) according to private key β₁₁,β₁₂,β₂₁,β₂₂,p₁,p₂, work as j>When 2, using formulaCalculating parameter (β₁₃,…,β_1n) and (β₂₃,…,β_2n).

(3-4-2) as j=1, calculateWith Obtain m₁For mould p₁p₂Under unique solution.

(3-4-3) as j=2 ..., h, calculateWithObtain m_jFor mould p₁p₂Under unique solution.

(3-4-4) as j=h+1, calculateWith Obtain m_h+1For mould p₁p₂Lower unique solution.

(3-4-5) work as j=h+2 ..., during n, calculateWith Obtain m_jFor mould p₁p₂Under unique solution.

Embodiment 2

Random parameter ε is obtained by synchronous method, this method comprises the steps：

(1) generate key.Further include following steps：

(1-1) adopt iterative manner construction k × n dimension non-singular matrix A.Further include following steps：

(1-1-1) determine k=2.

(1-1-2) 2 integer p in finite field Z, and finite field Z are chosen₁, p₂.

(1-1-3) following integer is chosen on finite field Z：(β₁₁,β₁₂)、(β₂₁,β₂₂) and (x₁,x₂).Make a₁₁=β₁₁,a₁₂ =β₁₂p₁,a₂₁=β₂₁,a₂₂=β₂₂p₂.

(1-1-4) structural matrix A=(a_ij), wherein, i=1,2, j=1 ..., n, j>When 2,

(1-2) pass through to obscure or diffusion way F obtains vectorial d=(d₁,d₂,…,d_j,…,d_n), wherein, d_jBy as follows Mode solves：

(A1) choose integer t, s, γ, c, δ, h are so as to meet following 3 conditions simultaneously：(a)γc-δ<max(s,t)<δ； (b)2.2<h<n-2；(c)gcd(R₁,R₃)=1.Wherein, R₁=δ (X+Y) m+c, R₃=1+ γ (X+Y) m, m=p₁p₂- 1, e= tp₁p₂-1.

Wherein,

Choose positive integer R₂, make R₂|(R₁- 1), gcd (R₂,R₃)=1, and R₂>C, structural matrix K_3×2And matrix D_2×3, choosing Select any positive integer z₁, z₂.

(A2) calculating matrix C=K A=(c_yj), y=1,2,3.

(A3) 3 integer P are chosen₁=R₁, P₂=R₂R₃, P₃=R₁R₃.

(A4) congruence equations are solvedIf P₁、P₂And P₃It is not coprime two-by-two, concrete calculating is public Formula is：

d_j=(s+ γ R₁-R₁R₃δ)a_1j+(s+t+γR₁-R₁R₃δ)a_2jmodN

(1-3) by d=(d₁,...,d_n) and h together as public key, by β₁₁,β₁₂,β₂₁,β₂₂,D,P₁,P₂,P₃,p₁,p₂, x₁,x₂, t is together as corresponding private key.

(2) use public key encryption.Further include following steps：

(2-1) obtain plaintext M=(m₁,m₂,…,m_j,…,m_n), selected random parameter ε.

(2-2) public key being obtained with step (1) is encrypted to plaintext, and obtaining ciphertext C is：

(3) deciphered with private key.Further include following steps：

(3-1) congruence equations are solved

(3-2) calculate

(3-3) ε is obtained by synchronous method.

Synchronous method has a lot, such as outer synchronization etc..Communicating pair can get parms ε in the synchronous case.

(3-4) pass through S_A1,S_A2Solve with ε and obtain plaintext M=(m₁,m₂,…,m_j,…,m_n).Further include to walk as follows Suddenly：

(3-4-1) according to private key β₁₁,β₁₂,β₂₁,β₂₂,_p1,_p2, work as j>When 2, using formulaCalculating parameter (β₁₃,…,β_1n) and (β₂₃,…,β_2n).

(3-4-2) as j=1, calculateWithObtain m₁For mould p₁p₂Under unique solution.

(3-4-3) as j=2 ..., h, calculateWith Obtain m_jFor mould p₁p₂Under unique solution.

(3-4-4) as j=h+1, calculateWith Obtain m_h+1For mould p₁p₂Under unique solution.

(3-4-5) work as j=h+2 ..., during n, calculateWith Obtain m_jFor mould p₁p₂Under unique solution.

Embodiment 3

This method comprises the steps：

(1) generate key.Further include following steps：

(1-1) adopt iterative manner construction k × n dimension non-singular matrix A.Further include following steps：

(1-1-1) k=2, n=4 are determined.

(1-1-2) 2 integer number p in finite field Z, and finite field Z are chosen₁=3, p₂=7.

(1-1-3) choose the following integer on finite field Z：β₁₁=28, β₁₂=10, β₂₁=345, β₂₂=52, x₁=5, x₂ =9.Make a₁₁=β₁₁p₁=84,a₂₁=β₂₁p₂=2415,

(1-1-4) structural matrix A=(a_ij), wherein, i=1,2, j=1 ..., 4, j>When 2,

(1-2) pass through to obscure or diffusion way F obtains vectorial d=(d₁,d₂,d₃,d₄), vectorial d_jAsk in the following way Solution：

(A1) structural matrix K_3×2And matrix D_2×3：

Choose integer t=1, s=4, γ=3, δ=2, h=2, c=1.

R₁=6393481, R₂=2, R₃=9590221.

(A2) calculating matrix C=K A=(c_yj), y=1,2,3.

(A3) 3 integer P are chosen₁=R₁, P₂=R₂R₃, P₃=R₁R₃：

P₁=6393481, P₂=19180442, P₃=61314895749301.

(A4) calculateObtain

D=[47931939468,50598021734,100754893236,47605871855]

(1-3) by d, N=122629791498602, h=2 together as public key, by β₁₁=28, β₁₂=10, β₂₁= 345, β₂₂=52, D, P₁=6393481, P₂=19180442, P₃=61314895749301, p₁=3, p₂=7, x₁=5, x₂= 9, t=1 as corresponding private key.

(2) use public key encryption.Further include following steps：

(2-1) given plaintext M=[1,11,3,2], selected random parameter ε=3 are set.

(2-2) public key being obtained with step (1) is encrypted to plaintext, and obtaining ciphertext C is：

(3) deciphered with private key.Further include following steps：

(3-1) calculate

(3-2) calculate

(3-3) ε is obtained by decryption method：

CalculateObtain ε=3.

(3-4) pass through S_A1,S_A2Solve with ε and obtain plaintext M=(m₁,m₂,…,m_j,…,m_n).Further include to walk as follows Suddenly：

(3-4-1) according to private key β₁₁,β₁₂,β₂₁,β₂₂,p₁,p₂, work as j>When 2, using formula Calculating parameter

(3-4-2) as j=1, calculateWith? m₁=1.

(3-4-3) as j=2, calculateWith Obtain m₂=11.

(3-4-4) as j=3, calculateWith Obtain m₃=3.

(3-4-5) as j=4, calculateWith? m₄=2.

As it will be easily appreciated by one skilled in the art that the foregoing is only presently preferred embodiments of the present invention, not in order to Limit the present invention, all any modification, equivalent and improvement made within the spirit and principles in the present invention etc., all should comprise Within protection scope of the present invention.

Claims (5)

1. a kind of multi-variable public key ciphering method is it is characterised in that comprise the steps：

(1) generate key, further include following steps：

Choose k integer p in finite field Z and finite field Z₁,p₂,…,p_i,…,p_k, wherein, i is the no more than positive integer of k；? Following integer is chosen on finite field Z：(β₁₁, β₁₂), (β₂₁, β₂₂) ..., (β_i1, β_i2),…,(β_k1,β_k2) and (x₁,x₂,…, x_i,…,x_k)；Construction and (β₁₁, β₁₂), (β₂₁, β₂₂) ..., (β_i1, β_i2) ..., (β_k1, β_k2) and p₁,p₂,,p_i,…,p_kRelated Two groups of parameters a₁₁,a₂₁,…,a_i1,…,a_k1And a₁₂,a₂₂,…,a_i2,…,a_k2, make a_i1And a_i2Binary length identical；

Construction k × n dimension non-singular matrix A=(a_ij), j=1 ..., n, wherein, j>When 2,

Structural matrix K_l×kAnd matrix D_k×lSo as to meet D K=λ E_k×k, and k >=l, wherein, E_k×kIt is unit matrix, λ is Arbitrarily nonzero integer；

Calculating matrix C=K A=(c_yj), y=1 ..., l, chooses positive integer h, 0 ＜ h ＜ n, determines the value of random parameter ε Scope [1, e], wherein,T is any positive integer；

Choose l integer P₁,...,P_l, meet inequalityObtain P₁,...,P_l's Least common multiple N；

Solve congruence equationsObtain vectorial d=(d₁,d₂,…,d_j,…,d_n)；

By d and h together as public key, or by d, h and N together as public key, corresponding private key at least includes (x₁,x₂,…, x_i,…,x_k)、p₁,p₂,…,p_i,…,p_k、P₁,...,P_l、(β₁₁,β₁₂),(β₂₁,β₂₂),…,(β_i1,β_i2) ..., (β_k1,β_k2) and D；

(2) use public key encryption, further include following steps：

Obtain plaintext M=(m₁,…,m_n), selected random parameter ε；

The public key being obtained with step (1) is encrypted to plaintext in the way of probability encryption, obtains ciphertext C；

(3) deciphered with private key, further include following steps：

Solve congruence equations

Calculate [S_A1… S_Ak]^T=D [C_P1… C_Pl]^T；

Random parameter ε is obtained by decryption method or synchronous method；

By (S_A1,…,S_Ak) and random parameter ε solve obtain plaintext M=(m₁,…,m_n).

2. multi-variable public key ciphering method as claimed in claim 1 is it is characterised in that in described step (1), a_i1=β_i1p_i,

3. multi-variable public key ciphering method as claimed in claim 1 is it is characterised in that in described step (1), a_i1=β_i1, a_i2 =β_i2p_i.

4. multi-variable public key ciphering method as claimed any one in claims 1 to 3 is it is characterised in that described ciphertext C is by such as Any one in lower expression formula obtains：

$C={\mathrm{\&Sigma;}}_{i=1}^h{d}_i{m}_i+{\mathrm{\&Sigma;}}_{i=h+1}^n{d}_i{m}_i\mathrm{\&epsiv;},$

$C={\mathrm{\&Sigma;}}_{i=1}^h{d}_i{m}_i+{\mathrm{\&Sigma;}}_{i=h+1}^n{d}_i{m}_i\mathrm{\&epsiv;}\mathrm{mod}N,$

With

$C={\mathrm{\&Sigma;}}_{i=1}^h{d}_i{m}_i+{\mathrm{\&Sigma;}}_{i=h+1}^n{d}_i{m}_i\mathrm{\&epsiv;}+\mathrm{\&epsiv;}\mathrm{mod}N.$

5. multi-variable public key ciphering method as claimed in claim 4 is it is characterised in that obtain random parameter by decryption method ε is specially：

Calculate congruence equationsObtain random parameter ε, wherein, | λ | represents that integer λ's is exhausted To value,The i-th row all elements sum for matrix D.